Solve for $x$ and $y$ using elimination. ${2x+2y = 24}$ ${-2x-5y = -36}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-3y = -12$ $\dfrac{-3y}{{-3}} = \dfrac{-12}{{-3}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x+2y = 24}\thinspace$ to find $x$ ${2x + 2}{(4)}{= 24}$ $2x+8 = 24$ $2x+8{-8} = 24{-8}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 4}$ into $\thinspace {-2x-5y = -36}\thinspace$ and get the same answer for $x$ : ${-2x - 5}{(4)}{= -36}$ ${x = 8}$